Knite, I believe you are correct, but in my researching online what the problem is, it appears that MANY different computers and MANY different TVs have many random irregularities and incompatibilities....
Even a perfectly normal PC could still have issues with an otherwise perfectly normal TV with HDMI inputs.
There are many people on the internet searching, asking, and looking for help on the same problem I had, and the main answer is "Sorry, it's just not working because of X, or because of Y" -- whereas you rarely hear that about DVI inputs.
I'm up in the air I guess. I wish they'd come up with better interfaces, what with higher and higher resolutions, what with eyefinity taking off, etc.